I still think you should not take her over to your mother's house until your mother is ready to let go of her anger/resentment toward your W. Trust me when I tell you it will not be good if you try this again, thinking it will be different the next time. Your W made an attempt and your mother made her cry. Why would you subject her to that when you knew how your mother felt? Ugh!
You will be caught in the middle. Your W will think you're taking up for the mother, and the mother will think you're defending the W. Both will be angry at You!
It is not about what you feel should work in your M. It is about doing the work that gets the right results. Do what works!